Tenichi is a high school boy but he's also a professional house cleaner. There's usually more than 1 solution to a problem. How about you work two days worth of cleaning on the 23rd, preparing meals, cleaning the bathroom, living room, cat cage etc so that Himari can work on the 24th without worry?
Unless he actually hasn't made up his mind on whom he wants to spend christmas with (which is honestly the most plausible case here).